1
JEE Main 2024 (Online) 8th April Morning Shift
Numerical
+4
-1

Let the area of the region enclosed by the curve $$y=\min \{\sin x, \cos x\}$$ and the $$x$$ axis between $$x=-\pi$$ to $$x=\pi$$ be $$A$$. Then $$A^2$$ is equal to __________.

2
JEE Main 2024 (Online) 5th April Morning Shift
Numerical
+4
-1

The area of the region enclosed by the parabolas $$y=x^2-5 x$$ and $$y=7 x-x^2$$ is ________.

3
JEE Main 2024 (Online) 1st February Evening Shift
Numerical
+4
-1
Three points $\mathrm{O}(0,0), \mathrm{P}\left(\mathrm{a}, \mathrm{a}^2\right), \mathrm{Q}\left(-\mathrm{b}, \mathrm{b}^2\right), \mathrm{a}>0, \mathrm{~b}>0$, are on the parabola $y=x^2$. Let $\mathrm{S}_1$ be the area of the region bounded by the line $\mathrm{PQ}$ and the parabola, and $\mathrm{S}_2$ be the area of the triangle $\mathrm{OPQ}$. If the minimum value of $\frac{\mathrm{S}_1}{\mathrm{~S}_2}$ is $\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ is equal to __________.
4
JEE Main 2024 (Online) 1st February Evening Shift
Numerical
+4
-1
The sum of squares of all possible values of $k$, for which area of the region bounded by the parabolas $2 y^2=\mathrm{k} x$ and $\mathrm{ky}^2=2(y-x)$ is maximum, is equal to :